# eccc_sim: Simulating an (E)CCC-GARCH(1,1) process In hoanguc3m/ccgarch: Conditional Correlation GARCH models

## Description

This function simulates data either from the original CCC-GARCH by Bollerslev (1990) or from the Extended CCC-GARCH that has non-zero off-diagonal entries in the parameter matrices in the GARCH equation. The innovations (the standardised residuals) can be either a normal or student's $t$ distribution.

The dimension (N) is determined by the number of elements in the \mathbf{a} vector.

## Usage

 1  eccc.sim(nobs, a, A, B, R, d.f=Inf, cut=1000, model) 

## Arguments

 nobs a number of observations to be simulated (T) a a vector of constants in the GARCH equation (N \times 1) A an ARCH parameter matrix in the GARCH equation. \mathbf{A} can be a diagonal matrix for the original CCC-GARCH model or a full matrix for the extended model (N \times N) B a GARCH parameter matrix in the GARCH equation. \mathbf{B} can be a diagonal matrix for the original CCC-GARCH model or a full matrix for the extended model (N \times N) R a constant conditional correlation matrix (N \times N) d.f the degrees of freedom parameter for the t-distribution cut the number of observations to be thrown away for removing initial effects of simulation model a character string describing the model. "diagonal" for the diagonal model and "extended" for the extended (full ARCH and GARCH parameter matrices) model

## Value

A list with components:

 h a matrix of the simulated conditional variances (T \times N) eps a matrix of the simulated time series with (E)CCC-GARCH process (T \times N)

## Note

When d.f=Inf, the innovations (the standardised residuals) follow the standard normal distribution. Otherwise, they follow a student's t-distribution with d.f degrees of freedom equal.

When model="diagonal", only the diagonal entries in \mathbf{A} and \mathbf{B} are used. If the ARCH and GARCH matrices do not satisfy the stationarity condition, the simulation is terminated.

## References

Bollerslev, T. (1990), “Modeling the Coherence in Short-Run Nominal Exchange Rates: A Multivariate Generalized ARCH Approach”, Review of Economics and Statistics, 72, 498–505.

Nakatani, T. and T. Ter\"asvirta (2009), “Testing for Volatility Interactions in the Constant Conditional Correlation GARCH Model”, Econometrics Journal, 12, 147–163.

Nakatani, T. and T. Ter\"asvirta (2008), “Appendix to Testing for Volatility Interactions in the Constant Conditional Correlation GARCH Model” Department of Economic Statistics, Stockholm School of Economics, available at http://swopec.hhs.se/hastef/abs/hastef0649.htm.

dcc.sim, stcc.sim
  1 2 3 4 5 6 7 8 9 10 11 12 # Simulating data from the original CCC-GARCH(1,1) process nobs <- 1000; cut <- 1000; nu <- 10 a <- c(0.003, 0.005, 0.001) A <- diag(c(0.2,0.3,0.15)) B <- diag(c(0.79, 0.6, 0.8)) R <- matrix(c(1.0, 0.4, 0.3, 0.4, 1.0, 0.12, 0.3, 0.12, 1.0),3,3) ## Not run: ccc.data <- eccc.sim(nobs,a, A, B, R, model="diagonal") ccc.data.t <- eccc.sim(nobs,a, A, B, R, d.f=nu, model="diagonal") ## End(Not run)